The overall objective of this project is to use and further develop the mathematical framework of transition-path theory (TPT; W. E and E. Vanden-Eijnden, Annu. Rev. Phys. Chem. 2010 61:391-420) to quantify rates of small molecule entry/exit and intramolecular diffusion in proteins. Based on all-atom molecular dynamics, the project combines free-energy reconstruction using single sweep, pathway estimation using zero-temperature string method, determination of the committor function, and milestoning calculations with isocommittor dividing surfaces. The focus is on drawing inferences regarding rate-determining mechanisms using the committor and on using isocommittor foliation to enhance the computational efficiency of milestoning for computing exact rates. We consider three major penetrant/protein systems: (i) CO/myoglobin; (ii) O2/monomeric sarcosine oxidase (MSOX); and (iii) H2O/aquaporin-1. In each case, rate quantification will serve to evaluate the relative contribution of putative entry/exit portals and transport pathways to overall kinetics. To date, no simulation methods have been published which predict rates of ligand entry and intramolecular transport. Importantly, TPT provides the theoretical basis for computing the committor function which is used in a statistical description of reactive trajectories. The key intellectual contribution of this project will be demonstrating the computation of the committor in above important protein/ligand systems as well as using it to identify rate-limiting mechanisms and to enhance the efficiency and accuracy of milestoning for computing exact rates. However, although TPT makes committor determination conceptually straightforward, it remains so far unresolved how best to compute it and then apply it in practice in large-scale biomolecular simulations. If successful, it is anticipated that these approaches will allow for meaningful evaluation of putative transport pathways and entry/exit portals when compared to experimental kinetic data.